[2]

It is not easy to describe the whole of Italy under any one geometrical figure; although some say that it is a promontory of triangular form, extending towards the south and winter rising, with its apex towards the Strait of Sicily, and its base formed by the Alps. . . . . . [No one can allow this definition either for the base or one of the sides,] although it is correct for the other side which terminates at the Strait, and is washed by the Tyrrhenian Sea. But a triangle, properly so called, is a rectilinear figure, whereas in this instance both the base and the sides are curved. So that, if I agree, I must add that the base and the sides are of a curved figure, and it must be conceded to me that the eastern side deviates, as well; otherwise they have not been sufficiently exact in describing as one side that which extends from the head of the Adriatic to the Strait [of Sicily]. For we designate as a side a line without any angle; now a line without any angle is one which does not incline to either side, or but very little; whereas the line from Ariminum1 to the Iapygian promontory,2 and that from the Strait [of Sicily] to the same promontory, incline very considerably. The same I consider to be the case with regard to the lines drawn from the head of the Adriatic and Iapygia, for meeting about the neighbourhood of Ariminum and Ravenna, they form an angle, or if not an angle, at least a strongly defined curve. Consequently, if the coast from the head [of the Adriatic] to Iapygia be considered as one side, it cannot be described as a right line; neither can the remainder of the line from hence to the Strait [of Sicily], though it may be considered another side, be said to form a right line. Thus the figure [of Italy] may be said to be rather quadrilateral than trilateral, and can never without impropriety be called a triangle. It is better to confess that you cannot define exactly ungeometrical figures.

1 Rimini.

2 Capo di Leuca.